If I don't finish a puzzle, I just close my web browser and reopen it later. Then I go to the list of recent games. It will have a "Retry" link next to the incomplete game. You only have 24 hours to do this, however. Then it's counted as a loss.

No, but when you get to the Retry area, the time has been running for the whole time you've been gone. Once you start a puzzle, the time starts. Closing the window will only make you have to start from scratch again the next time you do it. I know because when I was new here, I found I could retry puzzles and did. After I was done, I saw that I had spent over 2,000 minutes on one. That messed up my time on the scorecard. Not fun!